In 24 hours, House Democrats have gone from opposing the GOP proposal to tighten the United States' screening of Iraqi and Syrian refugees to supporting the bill in large numbers.

The shift is due to a number of factors, including pressure from constituents to take action this week — as well as frustration with the White House's inability to offer a compelling reason to wait. "What they should be doing is accepting the bill and offering to work with all of us on both sides to make it workable," said Rep. Gerald E. Connolly, D-Va., of administration officials.

President Barack Obama has threatened to veto the measure, which the Office of Management and Budget said "would introduce unnecessary and impractical requirements" on the vetting of refugees fleeing both war-torn Syria and Iraq who are victims of terrorism at the hands of the Islamic State.

Pelosi: Refugee Bill ‘Sends Wrong Message’

Connolly, who plans to vote for the GOP bill, left a Democratic whip meeting Thursday morning unsatisfied with the pitch he and his colleagues had just received from White House Chief of Staff Denis McDonough and Homeland Security Secretary Jeh Johnson.

"Frankly, my sense is more and more of my colleagues feel the same way," he said, adding there was a "lack of a compelling reason to vote 'no.'"

"It's not going over well," a House Democratic aide told CQ Roll Call as members continued to listen to McDonough and Johnson. "The message on this is too complicated."

Rep. Keith Ellison, D-Minn., an opponent of the GOP bill and one of two Muslims serving in the House, said he believes the White House has done "as good a job as can be done."

"If I was to offer [administration officials] some constructive proposals, it would be to say, 'help members see why the [Republican] bill is going to essentially raise a threshold so that nobody's gonna get certified. I mean, I think it's important to make that point a little more explicit."

The chamber will vote Thursday afternoon on the bill, crafted by Homeland Security Chairman Michael McCaul, R-Texas, and Rep. Richard Hudson, R-N.C., that would add additional layers of bureaucracy to the vetting process of Syrian and Iraqi refugees seeking entry into the U.S.

It will be the first of several planned legislative responses to the recent terrorist attack in Paris carried out by affiliates of the Islamic State, also known as ISIS or ISIL.

Democrats had originally chafed at what they considered the GOP's unwillingness to collaborate with the minority party.

Reps. Zoe Lofgren, D-Calif., and Bennie Thompson, D-Miss., proposed a leadership-backed alternative that would strengthen screening procedures but not entirely close entry to asylum seekers, which they contend would happen under the Republican bill.

Now, Democrats will have an opportunity to cast a procedural vote on this language on the floor Thursday in the form of a "motion to recommit."

But as the White House struggled to make its pitch, hopes for Democratic unity diminished. By Wednesday evening, the 15-member, fiscally conservative Blue Dog Coalition had abandoned its leadership.

A House Democrat, speaking on condition of anonymity to discuss private conversations, said there were progressives who entered the meeting with McDonough and Johnson prepared to oppose the McCaul-Hudson bill and left re-evaluating their position.

This member said the focus of McDonough and Johnson's message was the White House doesn't want to add an "extra burden" to the existing screening process, which the Obama administration strongly defends. "What member of Congress wants to go home to their district and say, 'I voted against this bill to keep you safe because I didn't want to impose more work on the bureaucracy?'" the lawmaker asked.

Hudson suggestion Johnson, the Homeland chief, was in a tough position.

"Jeh Johnson is a good man, but it’s a shame that in light of the comments he’s made about the concerns with vetting these refugees that he’s now carrying water for the president on the political side here, trying to keep Democrats from voting with the American people," Hudson told CQ Roll Call. "And so it’s unfortunate, but I think they will have a number of Democrats on the bill to move forward.”

Democratic leadership will not whip votes on the measure and Minority Leader Nancy Pelosi, D-Calif., told members they were free to vote however they wished.

"Nobody's asking you to do anything," was the message she relayed to her members, Pelosi told reporters Thursday. "Do whatever works for you, for your district."